===========================================================================================
This analysis explores the univariate, bivariate, & multivariate relationships between the variables in the provided tidy Red Wine data set using RStudio. The complete dataset can be found here.
First step is to load the data and do some basic assessments. This includes displaying the internal structure of the initial data frame.
## 'data.frame': 1599 obs. of 13 variables:
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ fixed.acidity : num 7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
## $ volatile.acidity : num 0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
## $ citric.acid : num 0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
## $ residual.sugar : num 1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
## $ chlorides : num 0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
## $ free.sulfur.dioxide : num 11 25 15 17 11 13 15 15 9 17 ...
## $ total.sulfur.dioxide: num 34 67 54 60 34 40 59 21 18 102 ...
## $ density : num 0.998 0.997 0.997 0.998 0.998 ...
## $ pH : num 3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
## $ sulphates : num 0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
## $ alcohol : num 9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
## $ quality : int 5 5 5 6 5 5 5 7 7 5 ...Next, programatically transformed the integer Quality data to a Factor, and output the head and tail results for review.
## [1] 5 5 5 6 5 5
## Levels: 3 < 4 < 5 < 6 < 7 < 8## [1] 6 5 6 6 5 6
## Levels: 3 < 4 < 5 < 6 < 7 < 8Generated a new Factored Variable named ‘Rating,’ and output the head and tail results for review.
## [1] average average average average average average
## Levels: bad < average < good## [1] average average average average average average
## Levels: bad < average < goodDisplay the internal structure after creating the new Factored Variable: Rating.
## 'data.frame': 1599 obs. of 13 variables:
## $ fixed.acidity : num 7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
## $ volatile.acidity : num 0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
## $ citric.acid : num 0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
## $ residual.sugar : num 1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
## $ chlorides : num 0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
## $ free.sulfur.dioxide : num 11 25 15 17 11 13 15 15 9 17 ...
## $ total.sulfur.dioxide: num 34 67 54 60 34 40 59 21 18 102 ...
## $ density : num 0.998 0.997 0.997 0.998 0.998 ...
## $ pH : num 3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
## $ sulphates : num 0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
## $ alcohol : num 9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
## $ quality : Ord.factor w/ 6 levels "3"<"4"<"5"<"6"<..: 3 3 3 4 3 3 3 5 5 3 ...
## $ rating : Ord.factor w/ 3 levels "bad"<"average"<..: 2 2 2 2 2 2 2 3 3 2 ...In addition, listed out the column (variable) names of interest for reference. Superfluous columns were excluded.
##
## * fixed.acidity
## * volatile.acidity
## * citric.acid
## * residual.sugar
## * chlorides
## * free.sulfur.dioxide
## * total.sulfur.dioxide
## * density
## * pH
## * sulphates
## * alcohol
## * quality
## * rating
##
## <!-- end of list -->Output of the head for selected columns.
## pH sulphates alcohol quality rating
## 1 3.51 0.56 9.4 5 average
## 2 3.20 0.68 9.8 5 average
## 3 3.26 0.65 9.8 5 average
## 4 3.16 0.58 9.8 6 average
## 5 3.51 0.56 9.4 5 averageOutput of the tail for selected columns.
## pH sulphates alcohol quality rating
## 1595 3.45 0.58 10.5 5 average
## 1596 3.52 0.76 11.2 6 average
## 1597 3.42 0.75 11.0 6 average
## 1598 3.57 0.71 10.2 5 average
## 1599 3.39 0.66 11.0 6 averageOutput of the Summary Statistics together with the Counts for the Factored Variables:
First lets plot the distribution of each variable to get a sense of the data. Now, lets remove some outliers and explore these individual univariate plots in detail!
Both distribution plots for pH and Density appear to be normally distributed.
The mean typically is equal to the median.
The distribution plots for alcohol, residual sugar, chlorides, free sulfur dioxide, total sulfur dioxide, and sulphates appear to be rightly skewed.
For a right skewed distribution, the mean is typically greater than the median. Also, the tail of the distribution on the right hand (positive) side is longer than on the left hand side.
The distribution plot for Citric Acid appears to be Bimodally Distributed.
In statistics, a bimodal distribution appears as distinct peaks.
Most of the wines in the dataset are average quality wines. I need to determine the main variables that are driving these results.
The Red Wine Dataset has 1599 rows and 13 columns. The categorical variables are ‘quality’ and ‘rating’, and the remainder are numerical variables that indicate the physical and chemical properties of the wine.
It was observed that most of the wines are categorized as ‘average’ quality with a few ‘bad’ and ‘good’ wines, respectively, in the tals. Also, all variables showed outliers. This suggests that the data is of poor predictive value.
My main point of interest in this dataset is the average ‘rating’, and why so many wines fell into that bucket. I would like to determine which factors determine the quality of a wine and what factors are critical for a good wine versus a bad wine.
The variables related to acidity (fixed, volatile, citric.acid and pH) might explain some of the variance. The different acid concentrations might affect the taste of the wine. Also,residual sugar determines how sweet a wine is, so it also may influence the taste.
A rating variable was created.
Citric.acid stood out from the other distributions. It had outliers and what appeared to be a bimodal distribution. Also, most of the variables were rightly skewed. Outliers were removed to confirm that the observed bimodal and skewed distributions were valid, and not the result of a few outliers.
##
##
## +--------------------------+---------------+------------------+-------------+
## | | fixed.acidity | volatile.acidity | citric.acid |
## +==========================+===============+==================+=============+
## | **fixed.acidity** | 1 | -0.26 | **0.67** |
## +--------------------------+---------------+------------------+-------------+
## | **volatile.acidity** | -0.26 | 1 | **-0.55** |
## +--------------------------+---------------+------------------+-------------+
## | **citric.acid** | **0.67** | **-0.55** | 1 |
## +--------------------------+---------------+------------------+-------------+
## | **residual.sugar** | 0.11 | 0 | 0.14 |
## +--------------------------+---------------+------------------+-------------+
## | **chlorides** | 0.09 | 0.06 | 0.2 |
## +--------------------------+---------------+------------------+-------------+
## | **free.sulfur.dioxide** | -0.15 | -0.01 | -0.06 |
## +--------------------------+---------------+------------------+-------------+
## | **total.sulfur.dioxide** | -0.11 | 0.08 | 0.04 |
## +--------------------------+---------------+------------------+-------------+
## | **density** | **0.67** | 0.02 | **0.36** |
## +--------------------------+---------------+------------------+-------------+
## | **pH** | **-0.68** | 0.23 | **-0.54** |
## +--------------------------+---------------+------------------+-------------+
## | **sulphates** | 0.18 | -0.26 | **0.31** |
## +--------------------------+---------------+------------------+-------------+
## | **alcohol** | -0.06 | -0.2 | 0.11 |
## +--------------------------+---------------+------------------+-------------+
## | **quality** | 0.12 | **-0.39** | 0.23 |
## +--------------------------+---------------+------------------+-------------+
##
## Table: Table continues below
##
##
##
## +--------------------------+----------------+-----------+
## | | residual.sugar | chlorides |
## +==========================+================+===========+
## | **fixed.acidity** | 0.11 | 0.09 |
## +--------------------------+----------------+-----------+
## | **volatile.acidity** | 0 | 0.06 |
## +--------------------------+----------------+-----------+
## | **citric.acid** | 0.14 | 0.2 |
## +--------------------------+----------------+-----------+
## | **residual.sugar** | 1 | 0.06 |
## +--------------------------+----------------+-----------+
## | **chlorides** | 0.06 | 1 |
## +--------------------------+----------------+-----------+
## | **free.sulfur.dioxide** | 0.19 | 0.01 |
## +--------------------------+----------------+-----------+
## | **total.sulfur.dioxide** | 0.2 | 0.05 |
## +--------------------------+----------------+-----------+
## | **density** | **0.36** | 0.2 |
## +--------------------------+----------------+-----------+
## | **pH** | -0.09 | -0.27 |
## +--------------------------+----------------+-----------+
## | **sulphates** | 0.01 | **0.37** |
## +--------------------------+----------------+-----------+
## | **alcohol** | 0.04 | -0.22 |
## +--------------------------+----------------+-----------+
## | **quality** | 0.01 | -0.13 |
## +--------------------------+----------------+-----------+
##
## Table: Table continues below
##
##
##
## +--------------------------+---------------------+----------------------+
## | | free.sulfur.dioxide | total.sulfur.dioxide |
## +==========================+=====================+======================+
## | **fixed.acidity** | -0.15 | -0.11 |
## +--------------------------+---------------------+----------------------+
## | **volatile.acidity** | -0.01 | 0.08 |
## +--------------------------+---------------------+----------------------+
## | **citric.acid** | -0.06 | 0.04 |
## +--------------------------+---------------------+----------------------+
## | **residual.sugar** | 0.19 | 0.2 |
## +--------------------------+---------------------+----------------------+
## | **chlorides** | 0.01 | 0.05 |
## +--------------------------+---------------------+----------------------+
## | **free.sulfur.dioxide** | 1 | **0.67** |
## +--------------------------+---------------------+----------------------+
## | **total.sulfur.dioxide** | **0.67** | 1 |
## +--------------------------+---------------------+----------------------+
## | **density** | -0.02 | 0.07 |
## +--------------------------+---------------------+----------------------+
## | **pH** | 0.07 | -0.07 |
## +--------------------------+---------------------+----------------------+
## | **sulphates** | 0.05 | 0.04 |
## +--------------------------+---------------------+----------------------+
## | **alcohol** | -0.07 | -0.21 |
## +--------------------------+---------------------+----------------------+
## | **quality** | -0.05 | -0.19 |
## +--------------------------+---------------------+----------------------+
##
## Table: Table continues below
##
##
##
## +--------------------------+-----------+-----------+-----------+----------+
## | | density | pH | sulphates | alcohol |
## +==========================+===========+===========+===========+==========+
## | **fixed.acidity** | **0.67** | **-0.68** | 0.18 | -0.06 |
## +--------------------------+-----------+-----------+-----------+----------+
## | **volatile.acidity** | 0.02 | 0.23 | -0.26 | -0.2 |
## +--------------------------+-----------+-----------+-----------+----------+
## | **citric.acid** | **0.36** | **-0.54** | **0.31** | 0.11 |
## +--------------------------+-----------+-----------+-----------+----------+
## | **residual.sugar** | **0.36** | -0.09 | 0.01 | 0.04 |
## +--------------------------+-----------+-----------+-----------+----------+
## | **chlorides** | 0.2 | -0.27 | **0.37** | -0.22 |
## +--------------------------+-----------+-----------+-----------+----------+
## | **free.sulfur.dioxide** | -0.02 | 0.07 | 0.05 | -0.07 |
## +--------------------------+-----------+-----------+-----------+----------+
## | **total.sulfur.dioxide** | 0.07 | -0.07 | 0.04 | -0.21 |
## +--------------------------+-----------+-----------+-----------+----------+
## | **density** | 1 | **-0.34** | 0.15 | **-0.5** |
## +--------------------------+-----------+-----------+-----------+----------+
## | **pH** | **-0.34** | 1 | -0.2 | 0.21 |
## +--------------------------+-----------+-----------+-----------+----------+
## | **sulphates** | 0.15 | -0.2 | 1 | 0.09 |
## +--------------------------+-----------+-----------+-----------+----------+
## | **alcohol** | **-0.5** | 0.21 | 0.09 | 1 |
## +--------------------------+-----------+-----------+-----------+----------+
## | **quality** | -0.17 | -0.06 | 0.25 | **0.48** |
## +--------------------------+-----------+-----------+-----------+----------+
##
## Table: Table continues below
##
##
##
## +--------------------------+-----------+
## | | quality |
## +==========================+===========+
## | **fixed.acidity** | 0.12 |
## +--------------------------+-----------+
## | **volatile.acidity** | **-0.39** |
## +--------------------------+-----------+
## | **citric.acid** | 0.23 |
## +--------------------------+-----------+
## | **residual.sugar** | 0.01 |
## +--------------------------+-----------+
## | **chlorides** | -0.13 |
## +--------------------------+-----------+
## | **free.sulfur.dioxide** | -0.05 |
## +--------------------------+-----------+
## | **total.sulfur.dioxide** | -0.19 |
## +--------------------------+-----------+
## | **density** | -0.17 |
## +--------------------------+-----------+
## | **pH** | -0.06 |
## +--------------------------+-----------+
## | **sulphates** | 0.25 |
## +--------------------------+-----------+
## | **alcohol** | **0.48** |
## +--------------------------+-----------+
## | **quality** | 1 |
## +--------------------------+-----------+Surprisingly residual sugar and quality had a very weak positive quality correlation of only 0.01. This suggests residual sugar impact on quality is negligible.
##
## --------------------------
## rating mean median
## --------- ------- --------
## bad 2.685 2.1
##
## average 2.504 2.2
##
## good 2.709 2.3
## --------------------------
##
## Table: Summaries for residual.sugar grouped by ratingVolatile acidity and quality have a -0.39 moderate negative correlation. This suggests red wine quality decreases as volatile acidity increases.
##
## ---------------------------
## rating mean median
## --------- -------- --------
## bad 0.7242 0.68
##
## average 0.5386 0.54
##
## good 0.4055 0.37
## ---------------------------
##
## Table: Summaries for volatile.acidity grouped by ratingHowever, fixed acidity and quality has a weak positive correlation of 0.11. Fixed Acidity may have some minimal impact on wine quality.
##
## --------------------------
## rating mean median
## --------- ------- --------
## bad 7.871 7.5
##
## average 8.254 7.8
##
## good 8.847 8.7
## --------------------------
##
## Table: Summaries for fixed.acidity grouped by ratingFurthermore, there are weak positive correlations for both (1) quality and sulphates at .25 and (2) quality and citric acid at .23. Also, ratings trends in the same direction for both. This suggests that better wines may have a stronger concentration of sulphates; and also, better wines may have higher citric acid.
##
## ---------------------------
## rating mean median
## --------- -------- --------
## bad 0.5922 0.56
##
## average 0.6473 0.61
##
## good 0.7435 0.74
## ---------------------------
##
## Table: Summaries for sulphates grouped by rating
##
## ---------------------------
## rating mean median
## --------- -------- --------
## bad 0.1737 0.08
##
## average 0.2583 0.24
##
## good 0.3765 0.4
## ---------------------------
##
## Table: Summaries for citric.acid grouped by ratingAs expected, citric acid and fixed acidity have a strong positive correlation of 0.67
Also, you can see a moderate negative correlation between volatile acidity and citric acid where the volatile acidity y values scale with the square root function. This is not so surprising given that we observed that red wine quality decreases as volatile acidity increases, and better wines have higher citric acid.
Running the Simpson function against citric acid and fixed acidity detected 7 clusters. Only two clusters correlated in the same direction as the group. The overall trend for the subgroups reversed or disappeared when the subgroups were combined.
Volatile acidity and quality have a -0.39 moderate negative correlation. This suggests red wine quality decreases as volatile acidity increases. However, fixed acidity and quality have a weak positive correlation. Fixed Acidity has almost no impact on wine quality. Furthermore, there are weak positive correlations for both (1) quality and sulphates and (2) quality and citric acid. Also, ratings trends in the same direction for both. This suggests that better wines have a stronger concentration of sulphates. Also, better wines have higher citric acid. As expected, citric acid and fixed acidity have a strong positive correlation of 0.67. Also, you can see a moderate negative correlation between volatile acidity and citric acid where the volatile acidity y values scale with the square root function. This is not so surprising given that we observed that red wine quality decreases as volatile acidity increases, and better wines have higher citric acid.
Simpson’s Paradox is a “phenomenon in probability and statistics, in which a trend appears in several different groups of data but disappears or reverses when these groups are combined.” Running the Simpson function against citric acid and fixed acidity detected 7 clusters. Only two clusters correlated in the same direction as the group. The overall trend for the subgroups reversed or disappeared when the subgroups were combined.
The strongest relationship this analysis focused on was that between citric acid and fixed volatility.
Lets use multivariate plots to answer some questions that came to light from the above bivariate plot analysis and to look for other relationships in the data.
pH measures acid concentration using a log scale. Therefore, there are stronger correlations between pH and the log of the acid concentrations. We use a linear model to investigate how much of the variance in pH is explained by citric acid, fixed acidity, and volatile acidity. With R-squared equal to 0.4876, it seems that the three acidity variables can only explain about half the variance in pH. This suggests there are other more relevant variables that affect acidity.
##
## Call:
## lm(formula = pH ~ I(log10(citric.acid)) + I(log10(volatile.acidity)) +
## I(log10(fixed.acidity)), data = subset(rw, citric.acid >
## 0))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.47184 -0.06318 -0.00003 0.06447 0.32265
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.230862 0.040578 104.266 < 2e-16 ***
## I(log10(citric.acid)) -0.052187 0.008797 -5.933 3.72e-09 ***
## I(log10(volatile.acidity)) -0.049788 0.021248 -2.343 0.0193 *
## I(log10(fixed.acidity)) -1.071983 0.038987 -27.496 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1068 on 1463 degrees of freedom
## Multiple R-squared: 0.4876, Adjusted R-squared: 0.4866
## F-statistic: 464.1 on 3 and 1463 DF, p-value: < 2.2e-16The plots below indicate that for wines with high alcohol content, having a higher concentration of sulphates produces better wines.
Also, the inverse seems to hold for acidity. For example, having less volatile acidity on higher concentrations of alcohol seems to produce better wines.
A few selected key variables (alcohol, sulphates, and acidity) were used to generate some linear models for comparison. The pH variable was excluded to avoid issues with perfect multicollinearity (also collinearity). Multicollinearity is a “phenomenon in which one predictor variable in a multiple regression model can be linearly predicted from the others with a substantial degree of accuracy.” The results were disappointing, with R-squared, the coefficient of determination statistic used to measure the proportion of the variance in the dependent variable that is explained by the independent variable(s), coming in low (highest reported R-square figure was .348)
##
## Calls:
## m1: lm(formula = as.numeric(quality) ~ alcohol, data = training_data)
## m2: lm(formula = as.numeric(quality) ~ alcohol + sulphates, data = training_data)
## m3: lm(formula = as.numeric(quality) ~ alcohol + sulphates + volatile.acidity,
## data = training_data)
## m4: lm(formula = as.numeric(quality) ~ alcohol + sulphates + volatile.acidity +
## citric.acid, data = training_data)
## m5: lm(formula = as.numeric(quality) ~ alcohol + sulphates + volatile.acidity +
## citric.acid + fixed.acidity, data = training_data)
## m6: lm(formula = as.numeric(quality) ~ alcohol + sulphates + pH,
## data = training_data)
##
## ====================================================================================================
## m1 m2 m3 m4 m5 m6
## ----------------------------------------------------------------------------------------------------
## (Intercept) -0.369 -0.877*** 0.197 0.227 -0.246 1.270*
## (0.228) (0.233) (0.255) (0.261) (0.292) (0.508)
## alcohol 0.384*** 0.370*** 0.341*** 0.341*** 0.352*** 0.396***
## (0.022) (0.021) (0.021) (0.021) (0.021) (0.022)
## sulphates 0.990*** 0.716*** 0.733*** 0.751*** 0.839***
## (0.135) (0.134) (0.138) (0.137) (0.138)
## volatile.acidity -1.115*** -1.152*** -1.239***
## (0.125) (0.145) (0.147)
## citric.acid -0.069 -0.509**
## (0.135) (0.183)
## fixed.acidity 0.061***
## (0.017)
## pH -0.699***
## (0.148)
## ----------------------------------------------------------------------------------------------------
## R-squared 0.245 0.285 0.339 0.339 0.348 0.301
## adj. R-squared 0.244 0.283 0.337 0.337 0.345 0.299
## sigma 0.712 0.694 0.667 0.667 0.663 0.686
## F 309.758 190.078 163.441 122.550 101.742 137.052
## p 0.000 0.000 0.000 0.000 0.000 0.000
## Log-likelihood -1034.673 -1008.598 -970.437 -970.308 -964.026 -997.448
## Deviance 485.816 460.103 424.905 424.790 419.262 449.528
## AIC 2075.346 2025.195 1950.874 1952.615 1942.053 2004.896
## BIC 2089.944 2044.659 1975.203 1981.810 1976.114 2029.226
## N 959 959 959 959 959 959
## ====================================================================================================
We used multivariate plots to answer some questions that came to light from the earlier bivariate plot analysis and to look for other relationships in the data. We know that pH measures acid concentration using a log scale; therefore, there are stronger correlations between pH and the log of the acid concentrations. We used a linear model to investigate how much of the variance in pH is explained by citric acid, fixed acidity, and volatile acidity. With R-squared equal to 0.4876, it seems that the three acidity variables can only explain about half the variance in pH. This suggests there are other more relevant variables that affect acidity.
It was shown that wines with high alcohol content, having a higher concentration of sulphates produces better wines. Also, the inverse seems to hold for acidity. For example, having less volatile acidity on higher concentrations of alcohol seems to produce better wines.
We also used some key variables (alcohol, sulphates, and acidity) to generate a few linear models for comparison. The pH variable was excluded to avoid issues with perfect multicollinearity (also collinearity). Multicollinearity is a “phenomenon in which one predictor variable in a multiple regression model can be linearly predicted from the others with a substantial degree of accuracy.” Also the low R-squared scores suggest that there are missing variables that can be better used to predict quality.
For my initial analysis, originally a table was used to display all the correlations for the red wine data set; but plotting the correlation matrix makes it even easier to identify both positive and negative correlations greater than an absolute value of 0.2.
This plot shows that the best quality wines have high concentrations fof both alcohol and sulphates. This implies that high alcohol contents and high sulphate concentrations together seem to produce better wines. This is something to definitely look for when shopping for red wines.
The linear model with the highest R-squared value could only explain approximately 35% of the variance in quality. This plot suggests that there are missing variables needed to better predict quality wines.
This analysis explored the univariate, bivariate, & multivariate relationships between the variables in the provided tidy Red Wine data set The data set contained information on the chemical properties of a selection of red wines. Also, a new Factored Variable named ‘Rating’ was added.
The first step was to do a univariate analysis of all the variables. A series of plots showed which variables were normally distributed and skewed. Focusing on the plots for quality and ratings showed that most wines in the dataset were of average quality. Why?
Continuing with the bivariate analysis it was shown that better wines have a stronger concentration of sulphates, together with higher counts of citric acid. Then following through with a multivariate analysis it was shown that wines with high alcohol content and having a higher concentration of sulphates produced better wines. Also, the inverse seemed to hold for acidity. For example, having less volatile acidity on higher concentrations of alcohol seemed to produce better wines. However, the generated liniear models using the alcohol, sulphates, and acidity variables did not well explain the variance in quality.
Future studies, should include larger data sets and more variables. For example, a winefolly.com article speaks to the importance of differences in tastes between unoaked versus oaked wines and the role the aging process plays in a wine’s malic acid conversion to lactic acid. Also, the data set can include categorized wine critic reviews and ratings, to determine if relying on such critical ratings can truly lead to selecting better tasting wines.
**https://cran.r-project.org/web/packages/gridExtra/vignettes/tableGrob.html**
**https://rapporter.github.io/pander/pandoc_table.html**
**https://github.com/pcasaretto/udacity-eda-project/blob/master/wine.Rmd**
**http://www.sthda.com/english/wiki/ggplot2-colors-how-to-change-colors-automatically-and-manually**
**https://rpubs.com/jasonmedina/219996**
**https://github.com/pcasaretto/udacity-eda-project/blob/master/wine.Rmd**